Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients

In this work, a greedy algorithm for the design of sparse linear-phase finite impulse response filters wherein the coefficients are successively fixed to zero individually is proposed. To meet the filter specifications, the coefficient for which the middle value of its feasible range is closest to zero is selected to be set to zero, whereas all the other unfixed coefficients are free to change. Design examples show that the proposed technique can design FIR filters with higher sparsity than that obtained by existing nonexhaustive algorithms for given specifications. To show the optimality of the algorithm, we design 100 filters, with results showing that the global optimal solution, i.e., the sparsest solution found by exhaustive search, can be achieved in most cases, but with much less computation time.